For the qustion given above, the following are sentences:
1. Each winter, I go ice skating with friends from my neighborhood.
2. We hurry to the ice.
3. Try to catch each other.
4. Sometimes I fall down.
The only fragment out of all the statement given is this:
And skate as fast as possible.
A simple sentence and an independent clause have one characteristic in common; the two of them express complete thoughts, that is, they can stand on their own as a sentence which expresses a complete thought. Dependent clauses and phrases on the other hand are known as fragments, this is because, they do not possess one or two of the constituents such as predicate, subjects, etc, that are needed to form a complete sentence. Thus, the fragment in the question given above does not express a complete thought.
